How would I integrate a texture with a particle 'carpet'?
It's quite simple to do using object coordinates.
Make a material for your particles and the rug that uses &quot;object&quot; for the texture coordinate, and set the object at the bottom of the node to your rug mesh (or an empty if you prefer). Then just adjust the scale until it looks the way you need.
Attached is an image that uses the same principle to map an image to an array of cubes.

In this example, the array of cubes is all one object (named cube), but this method works with any number of separate objects as well. Since setting an object in the Texture coordinates node sets that object as the source to do the mapping from. Just make sure the origin of the object is where you need it to be. You'll also have to play around with the texture scale to get it exactly how you need. But if you have the rug mesh and the particles using the same material and coordinates, they won't get out of sync.
Lastly, if you have a separate object be the source, moving the objects with the material won't move the texture, so the object will move, but the texture won't. Kind of like &quot;unmoving plaid&quot; if you've seen that effect before. But as long as the source moves with the textured object, you won't have that problem.